U.S. patent application number 13/056051 was filed with the patent office on 2011-12-22 for spatially distorted image.
Invention is credited to Gerd Ecker, Sandra Ecker, Klaus Wedrich.
Application Number | 20110308119 13/056051 |
Document ID | / |
Family ID | 40451381 |
Filed Date | 2011-12-22 |
United States Patent
Application |
20110308119 |
Kind Code |
A1 |
Ecker; Gerd ; et
al. |
December 22, 2011 |
SPATIALLY DISTORTED IMAGE
Abstract
The invention relates to a warped or curved surface with an
image visible from a reference point which is not an element of the
said surface, where the reference point has fixed position with
respect to the said surface, and the image on the said surface is
distorted in a way to provide an undistorted view on the said image
from the said reference point.
Inventors: |
Ecker; Gerd; (Alzey, DE)
; Ecker; Sandra; (Kaiserslautern, DE) ; Wedrich;
Klaus; (Engelstadt, DE) |
Family ID: |
40451381 |
Appl. No.: |
13/056051 |
Filed: |
July 29, 2009 |
PCT Filed: |
July 29, 2009 |
PCT NO: |
PCT/EP2009/059776 |
371 Date: |
March 30, 2011 |
Current U.S.
Class: |
40/427 ; 156/230;
427/256 |
Current CPC
Class: |
G06Q 30/02 20130101;
G09F 21/04 20130101; G09F 19/12 20130101 |
Class at
Publication: |
40/427 ; 427/256;
156/230 |
International
Class: |
G09F 19/12 20060101
G09F019/12; B44C 1/165 20060101 B44C001/165; B05D 5/06 20060101
B05D005/06 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 31, 2008 |
DE |
PCT/DE2008/001265 |
Claims
1.-9. (canceled)
10. A warped or curved surface with an image visible from a
reference point which is not an element of the said surface,
wherein the reference point has a fixed position with respect to
the said surface, and the image on the said surface is distorted in
a way to provide an undistorted view on the said image from the
said reference point.
11. The warped or curved surface with a distorted image of claim
10, wherein the distortion of the image on the said surface is such
that an undistorted image is generated on a focal plane by a
focussing means which focussing means has a fixed position with
respect to the reference point.
12. The warped or curved surface with a distorted image of claim
11, wherein the focussing means is an optical lens or a mirror.
13. A method of applying a distorted image on a warped or curved
surface to provide the warped or curved surface of claim 11,
comprising the steps of generating the coordinates of a plurality
of points P.sub.i which are elements of the said warped or curved
surface, the points P.sub.i being chosen such that they form a
plurality of equilateral triangles or squares, and that the square
distance between a point on the warped or curved surface whose
vertical projection onto the nearest triangle or square is in the
center of the said triangle or square, and the center point of the
said triangle or square is not larger than the area of the said
triangle or square multiplied by a resolution factor RF,
calculating for each of these points P.sub.i the colour information
comprising lightness, saturation, and hue from the undistorted
image in the focal plane, and applying to each of the points
P.sub.i on the said warped or curved surface a coloured dot having
the colour information as calculated in the second step.
14. The method of claim 13, wherein a coloured dot is applied with
an ink jet printing head.
15. The method of claim 13, wherein a coloured dot is applied with
a paint spray gun.
16. The method of claim 13, wherein a coloured dot is applied by
attaching a printed film onto the warped or curved surface.
17. The method of claim 16, wherein the printed film is cut with a
computer cutting tool so as to minimise overlap before application
thereof to the said warped or curved surface.
18. The method of claim 17, wherein the computer cutting tool is
programmed using the coordinate information of step 1 of claim 13.
Description
FIELD OF THE INVENTION
[0001] The invention relates to the graphic design of a curved or
warped surface with an image comprising lettering or pictures or
both, wherein the graphic design is an image distorted in
accordance with the curvature of the surface so that a view from a
defined location appears undistorted.
BACKGROUND OF THE INVENTION
[0002] Distorted graphics have been described in the prior art,
such as images from three-dimensional objects which are printed on
a plane or an adhesive film which is subsequently attached to a
plane, or painted on a substantially plane surface such as a lawn
or a textile which is placed on the ground, in DE 198 37 887 A1.
The origin of the picture in this case is mandatorily
three-dimensional. The process described is governed by
determination of angles, positioning of offset rods, or measuring
staffs, and mathematical formulae.
[0003] In WO 98/43 231, a figurative print is printed on a plane
carrier which print is comprised of at least a primary figurative
element and optionally, a secondary figurative element which is a
shadow or a relief or another three-dimensional effect element of
the first figurative element. All prints are plane.
[0004] In EP 1 418 561 B1, corresponding to the utility model DE
203 17 063, a method of generating an advertisement print is
disclosed where an advertisement print is printed on a plane
carrier with a predefined surface area, the print being distorted
so that printed letters appear to stand upright.
[0005] In EP 1 580 710 A2, an advertising board is described that
bears an advertising image, such as a picture or lettering, which
image comprises a first two-dimensional representation of the
image, and a second two-dimensional representation of the same
image, the two representations having an offset chosen such that
there is a three-dimensional impression generated.
SUMMARY OF THE INVENTION
[0006] There has not been a method disclosed yet to provide a
warped or curved surface with an image, where the image is
distorted in a way to provide an undistorted view from a given
point, for example when viewed by a camera.
[0007] It is therefore an object of the invention to provide a
method of generating an image on a spatially warped or curved
surface, particularly a surface that has an irregular spatial
shape, which cannot be exactly described by a mathematical formula,
such as a spherical or toroidical or ellipsoidal surface.
[0008] This object has been realised by providing a warped or
curved surface with image elements that are distinguished from the
background by their colour, viz., at least one of their lightness,
saturation and hue. Each of these image elements which make up the
image, which may be dots, or lines, or areas, the latter two being
formed by adjacent dots, in a linear, or an areal manner, where
adjacent dots preferably have the same colour, or at least a colour
that is different from that of the surrounding region, generally
referred to as "background", is characterised by its coordinates in
three dimensions, and by its colour properties, lightness,
saturation, and hue.
[0009] A further object is to provide a method of assigning the
correct colour information to each of the dots characterised by its
coordinates in three dimensions, and to apply this information to
the dot by printing or spraying, or to simultaneously apply the
colour information to more than one dot by applying the colour
information to a plastic film which film may be drawable or
shrinkable in a predetermined way, or which preferably is cut to
size, and applied to the warped or curved surface in a
predetermined way so that each of the dots on the warped or curved
surface bears the correct colour information.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0010] For each of the image elements, the following information
has to be provided:
[0011] The three-dimensional coordinates of each point P.sub.i of
the warped or curved surface where image elements shall be
assigned, all of the image elements forming the image that is
viewed from a chosen point or reference point, R.
[0012] For the sake of convenience, this chosen point or reference
point R is assigned the relative coordinates (0; 0; 0) in a
Cartesian system. Each point of the curved or warped surface can be
defined by the relative coordinates in relation to this reference
point, R=(0; 0; 0).
[0013] In accordance with the present invention, a warped or curved
surface is provided with an image visible from a reference point R
which is not an element of the image area of the said image on the
said surface, characterised in that the reference point preferably
has a fixed position with respect to the said surface, and the
image on the said surface is distorted in a way to provide an
undistorted view on the said image from the said reference
point.
[0014] Preferably, the distortion of the image on the said surface
is such that an undistorted image is generated on a focal plane by
a focussing means which focussing means preferably has a fixed
position with respect to the reference point.
[0015] Preferably, the focussing means is an optical lens.
Depending on the distance between lens and the image of the warped
or curved surface, it is also possible to use a Fresnel type lens.
Mirrors may, of course, also be used.
[0016] In accordance with the present invention, a method is also
provided to apply a distorted image on a warped or curved surface,
which method comprises the steps of generating the coordinates of a
plurality of points P.sub.i which are elements of the said warped
or curved surface, the points P.sub.i being chosen such that they
form a plurality of equilateral triangles or squares, or other,
preferably regular, polygons that can be used to assemble the said
warped or curved surface, and that the square distance between a
point on the warped or curved surface whose vertical projection
onto the nearest triangle or square or other polygon is in the
centre of the said triangle or square or other polygon, and the
centre point of the said triangle or square is not larger than the
area of the said triangle or square multiplied by a resolution
factor RF, calculating for each of these points P.sub.i the colour
information comprising lightness, saturation, and hue from the
undistorted image in the focal plane, and applying to each of the
points P.sub.i on the said warped or curved surface a coloured dot
having the colour information as calculated in the second step.
[0017] Preferably, this resolution factor RF is between 5 and 0.1,
a lower resolution factor giving a better resolution, which is
preferred in the case of the image comprising, or substantially
consisting of lettering which must, of course, be readable. For a
better resolution (lower resolution factor), the meshes of the
three-dimensional grid formed by the points P become narrower. A
resolution factor higher than 5 will lead to an image with low
resolution, with pixels to be seen, not fit for legible lettering,
while a lower resolution factor than 0.1 will render the grid
approximation of the warped or curved surface very complicated,
will lead to very high computing effort and very small mesh
width.
[0018] The coloured dots can be applied with an ink jet printing
head, or a paint spray gun, or similar means. A preferred method is
to apply coloured dots by computer-aided painting or printing where
spatial and colour coordinates are used to control the application
of coloured paint or ink onto the surface. A particularly preferred
method is attaching a printed film onto the warped or curved
surface. Such films can easily be replaced, and do not need special
treatment like thermal or irradiation crosslinking in the case of
paints, or protection against mechanical abrasion or the effect of
organic solvents like petrol, or gasoline, like in the case of ink
jet printing.
[0019] Resilient films like polyester based or polypropylene based,
or polyvinylchloride based films are particularly preferred. For
printing on the films, a further transformation is, of course
needed, which correlates each point P.sub.i on the warped or curved
surface with a point on the film which film is flat when
printed.
[0020] Preferably, the printed film is cut with a
computer-controlled cutting tool so as to minimise overlap before
application thereof to the said warped or curved surface. In this
case, the computer-controlled cutting tool is preferably programmed
using the coordinate information of the first step of the process
as described supra.
[0021] Coordinate information for the individual points P.sub.i
making up the warped or curved surface can be provided by simple
calculation if the shape of the warped or curved surface is
available from CAD data (Computer-Aided Design). The shape of the
surface can then be viewed in the form of a three-dimensional grid,
where each of the grid points P.sub.gi is characterised by its
coordinates (x.sub.gi; y.sub.gi; z.sub.gi) relative to the
reference point R.
[0022] In most real cases, however, the CAD data which may have
been a guidance for shaping the warped or curved surface do not
fully coincide with the real dimensions of the said surface. This
is the case, particularly, if a car body of a racing car is made
from fibre-reinforced thermoset or thermoplastic material which may
shrink unevenly upon curing or solidification, and therefore
deviate in its shape from the target shape, or desired values. It
may, of course also be the case that there are no CAD guiding data
available at all.
[0023] In such cases, the shape of the surface where the image
elements shall be applied may be measured by mechanical means (such
as with a stylus instrument), by optical means (such as laser
holography, interferometry), or by combination of any of these
methods, as provided by the state of the art, and described, by
construction of a grid similar to that provided by CAD data.
Depending on the desired resolution, the mesh size of the grid will
be chosen accordingly.
[0024] In the next step, a projection has to be made for each dot
P.sub.j(x.sub.j; y.sub.j; z.sub.j) which makes up the image in the
focal or imaging plane of the camera via the focussing element
(lens or mirror) of the camera onto the warped or curved surface to
its corresponding dot P.sub.i(x.sub.i; y.sub.i; z.sub.i). This
projection is performed with the usual means of analytical
geometry, by simple transformation. The difference with regard to
the known methods from the prior art is that not all dots P.sub.i
lie in the same plane, but have different distances to the
reference point, distances not being constant, nor being steadily
increasing or decreasing as is the case with a plane projection
surface.
[0025] The warped or curved surface can preferably be approximated
by a plurality of plane triangles or plane squares as area
elements, the length of the edges thereof being chosen according to
the desired resolution. It is also possible with smaller errors, to
approximate the warped or curved surface by a plurality of concave
or convex spherical or ellipsoidal surface elements which are
chosen such that there is no discontinuity or at least no
discontinuity larger than a preset value, in curvature at the
borders of the concave or convex spherical or ellipsoidal surface
elements.
[0026] For easier understanding, the following explanation starts
from the image that is constructed in a camera consisting of the
dots or points P.sub.j which corresponds to the image viewed from
the reference point, such as an on-board camera in a racing car.
These dots or points P.sub.j have now to be projected onto the
warped or curved surface. Each of these points or dots is fully
characterised by the set of spatial coordinates with respect to a
fixed point, and by its colour coordinates.
[0027] If the warped or curved surface is approximated by a
plurality of spherical surface elements, as shown in FIG. 1 for one
spherical element only, for the sake of clarity, a fictitious
letter "A", denoted as 2, viewed upright and undistorted, in a
plane parallel to the focal plane of a camera, by camera 1, the
image of it being, as known by the person skilled in the art,
laterally reversed and upside down, in the focal plane of the
camera, is shown distorted in the spherical element 3 of the warped
or curved surface.
[0028] In the case of approximation of the curved surface by a
plurality of triangles, this projection is as depicted in FIG. 2.
FIG. 2a shows a flat triangular surface element E of the warped or
curved surface. FIG. 2b shows a projection of the image 2' onto an
area element which is a plane square on the warped or curved
surface, the square constituting an individual plane element in the
grid of the said warped or curved surface. It is seen in what way
the letter "A" is distorted by the projection onto the said square
surface element on the warped or curved surface. In a similar way,
a sample lettering consisting of the three letters "A", "K", and
"Z", as viewed undistorted in the camera as 2'', is distorted as
3'', as shown in FIG. 2c.
[0029] In the cases of these approximations, or decompositions, of
the warped or curved surface into a plurality of surface elements,
having square, or triangular, or spherical shape, calculation of
the needed distortion is possible with the means of analytical
geometry.
[0030] Referring now to FIGS. 2a and 2b, the following
abbreviations are used for a triangular surface element as shown in
FIG. 2a, with an auxiliary orthogonal coordinate system with the
axes symmetrically touching the corners of a equilateral triangle,
the corners of which being referred to as a, b, and c, the side
lengths s= ab= bc= ca (the length s of a side of the equilateral
triangle between points a and b, points b and c, and points c and a
where a, b, and c are the corner points defining the equilateral
triangle), and the origin of the auxiliary coordinate system being
a point in space with equal distance to the three corner points of
the said triangle, viz., a, b, c, where
a = ( 1 2 2 s ; 0 ; 0 ) , b = ( 0 ; 1 2 2 s ; 0 ) , and c = ( 0 ; 0
; 1 2 2 s ) : ##EQU00001## .lamda. = 1 ( 1 / a 2 + 1 / b 2 + 1 / c
2 ) 1 2 ##EQU00001.2## and ##EQU00001.3## .alpha. = .lamda. / a ;
.beta. = .lamda. / b ; and .gamma. = .lamda. / c .
##EQU00001.4##
[0031] Any dot P.sub.j (x.sub.j; y.sub.j; z.sub.j) of a figure F in
FIG. 2b (in this case the letter "A", item 2') in the focal plane
of a camera corresponds to a dot P.sub.i(x.sub.i; y.sub.i; z.sub.i)
on a plane square area element E of a warped or curved surface,
where the coordinates of the said dot P.sub.i with relation to the
auxiliary coordinate system as described supra are
x.sub.i=(1+.alpha..sup.2/[.gamma.(1+.gamma.)])x.sub.j+.alpha..beta./[.ga-
mma.(1+.gamma.)])y.sub.j,
y.sub.i=.alpha..beta./[.gamma.(1+.gamma.)])x.sub.j+(1+.alpha..sup.2/[.ga-
mma.(1+.gamma.)])y.sub.j, and
z.sub.i=z.sub.j+d,
for all dots of the figure F' on the area element E, also referred
to as 3', of the warped or curved surface. The plane square
intersects the planes of the coordinate system as shown in FIG. 2a,
thereby forming the equilateral triangle which is shown in FIG.
2a.
[0032] In a first approximation, the distance d for each of the
individual surface elements can be regarded as constant within the
said surface element, as the distance from the focal plane to the
object F' is large in comparison to the distances in x- and
y-directions between the individual dots in the focal plane. For
short distances between focal plane and image, an exact calculation
has to be used.
[0033] This figure F' on the area element E of the warped or curved
surface can now be seen undistorted, as its image F in the said
focal plane of the said camera.
[0034] FIG. 3 shows a view of a racing car, with lettering on plane
surfaces. There remain many surfaces marked as 6, 6', 6'', 6'''
that are warped or curved, which have not yet been used for
advertisement purposes due to the restricted visibility. It is
possible, with the distorted images according to the present
application, to use these hitherto unused regions for advertisement
purposes.
[0035] FIG. 4 shows another view onto surfaces of a racing car
marked as 7, 7', 7'', and 7''' that are warped or curved, and which
have not yet been used for advertisement purposes due to restricted
visibility. It is also possible, with the distorted images
according to the present application, to use these hitherto unused
regions for advertisement purposes.
LIST OF REFERENCE NUMERALS
[0036] 1 on-board camera [0037] 2, 2', 2'' undistorted text [0038]
3, 3', 3'' distorted text [0039] x, y, z axes in a Cartesian system
of coordinates [0040] E plane [0041] a, b, c axis intersections of
a triangular surface element (x-, y- and z-axes) [0042] 5, 5'
positions for on-board cameras [0043] 6, 6', 6'', 6''' positions
for advertisement images according to the invention [0044] 7, 7',
7'', 7''' positions for advertisement images according to the
invention
* * * * *